Shape-changing mechanical metamaterials have drawn the attention of researchers toward the development of continuous-range tunable frequency selective surfaces (FSSs). In this paper, a novel tunable FSS utilizing an origami-inspired “eggbox” structure is presented featuring four-degrees of freedom that can change the frequency response of two orthogonal linear polarizations. The centrosymmetric “eggbox” structure can be folded or rotated along two axes that lead to unprecedented reconfigurability compared to traditional Miura-Ori-based structures which have fewer degrees of control. The utilized cross-shaped dipole FSS element shows enhanced bandwidth, support for orthogonal linear polarization, and ease of fabrication. The prototype is fabricated using a low-cost fully additive inkjet printing process with silver nanoparticle conductive ink. The outcome of this study shows a 25% frequency tunable range over two polarization directions. The design can be an ideal spatial filtering candidate for advanced ultra-wideband terrestrial and space applications.